The Gunners took the lead through Laurent Koscielny in the first half but Johan Djourou was sent off with just over 10 minutes remaining giving Fulham the ascendency to score twice late through Steve Sidwell and Bobby Zamora in injury time to move to 13th on the table.
Arsenal looked menacing from the start and took a deserved lead in the 21st minute when Aaron Ramsey's deflected dink into the area found Koscielny who headed home with consummate ease from the edge of the six-yard box for his first of the campaign and third Premier League goal for the Gunners.
Arsenal were reduced to ten men when Djourou was shown a second yellow card for a foul on Zamora in the 78th minute and it came back to bite the Gunners when Steve Sidwell headed home a leveler with five minutes remaining. Wojciech Szczesny's punch from a corner went only as far as Philippe Senderos who sent a header towards the goal-line where Sidwell was on hand to nod home the equaliser.
The one-man advantage was even more evident when Zamora hit a sweet volley for his first goal in a dozen games to give Fulham the victory in injury time after Sebastian Squillaci's header was not powerful enough to clear the area.
Arsenal were not without their chances throughout proceedings with a wasteful Gervinho missing two opportunities early but lashed his first attempt over the crossbar before missing the target from close range when Robin van Persie's corner found him at the back post.
In the 10th minute, Zamora forced a diving save from Szczesny five minutes before Brede Hangeland header over moments after John Arne Riise's ball for an unmarked Zamora was inches away from giving the Fulham striker a tap-in.
One of the most defining moments of the contest came in the 23rd minute when Fulham gloveman David Stockdale came up with two superb saves in quick succession to keep Fulham in the contest when he denied Aaron Ramsey and then Alex Song before Gervinho lashed across goal in what was a huge play by the home keeper.
Just after the half-hour mark, Bryan Ruiz almost produced a stunning individual goal when he beat off Song before advancing into the area but only saw his curling shot go wide before van Persie's flick with the outside of his right foot was well-held by Stockdale.
In the 64th minute, Senderos' header from Danny Murphy's free-kick sent some shivers through the Arsenal camp moments before Clint Dempsey rose above Per Mertesacker to send Bryan Ruiz's cross agonisingly wide with Szczesny at bay.
With 15 minutes left, Szczesny produced a top-drawer save when Ruiz was through on goal with the Pole denying the Costa Rican minutes before the Djourou decision which gave Martin Jol's men the impetus to complete a come-from-behind victory which is sure to frustrate Arsene Wenger's players who missed the chance to go clear of Chelsea in fourth.
Craven Cottage, London
Yellow cards:FUL - nil ARS - Johan Djourou 63'/78'
Red cards:ARS - Johan Djourou 78'